In photography it is not possible to take panoramic images with all cameras. To take a panoramic image usually requires a wide angle lens. One way of creating a panoramic image from a series of images is by a method called stitching. The individual images are captured with some overlap to allow proper registration. The images are preferably taken from the same location.
Proper registration may include transforms for correction of optical distortions as well as improper leveling induced by the user operating a hand held camera. While those corrections are commonly handled in stitching software there is another problem that cannot be corrected easily.
If the images are not taken from exactly the same location and if there is both a foreground and a background in the image, a new problem may occur. Even if it is possible to stitch the images in respect to the background, the foreground from the two images may not line up correctly. This problem is called internal parallax. This problem will be described in more detail below.
FIG. 1 illustrates a lens 100 comprised in a camera with a first nodal plane 101, an axis 102 and a focal plane 103. The first nodal plane 101 intersects the axis 102 at a first principal point 104. Two objects, object A 105 and object B 106, are placed at different distances from the lens 100. The objects are pictured at the focal plane 103. FIG. 2 illustrates the resulting image at the focal plane 103. Object A 105 can be seen behind object B 106.
In FIG. 3 the camera, and consequently the lens 100, is turned around the first principal point 104. The two objects 105, 106 are still situated on a straight line 300 that is passing through the first principal point 104. The image of the two objects 105, 106 at the focal plane 103 will look just the same as for the arrangement of FIG. 2 except that the objects will now appear closer to the edge of the image while they appeared in the center in the example described with relation to FIG. 1.
In FIG. 4 the camera is now turned around a point p 400 as opposed to the first principal point 104 in FIG. 1. Note that the two objects 105,106 are not aligned on the same line crossing the first nodal point 104. The two lines C1 401 and C2 402 that mark the centers of the objects now hit the focal plane 103 with a slight separation. In the image at the focal plane 103 object b 106 that is closer to the camera will not line up with object a 105 that is further away from the camera. This is illustrated in FIG. 5.
From the description in relation to FIGS. 1 to 5 it can be understood that we can only produce a perfectly stitched image if the camera was rotated around the first principal point 104 of the lens 100. This is of course impossible to do when holding the camera by hand. Even when the camera is mounted on a tripod it must be precisely aligned and calibrated.